Singlemolecule biophysics' Principles and objectives

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Single-molecule biophysics. Principles and
objectives

• Lecture 7
• September 22th

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For this week!
Your topic of the semester report. A great
attention has to be given on the quality of
writing, a solid outline, good questions and big
daunting challenges in the field, prospects,
updated references.
Lets think for a target talk (seminar). The
topic has to be discussed prior in the class.
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Outline

• Review material from Lecture 6
• transition state theory and reaction kinetics
• Single-molecule biophysics
• Motivation
• Aims and Principles
• Perspectives for other areas

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Reaction-Energy Diagrams

• For a one-step reactionreactants ? transition
  state ? products
• A catalyst lowers the energy of the transition
  state.

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Energy Diagram for a Two-Step Reaction

• Reactants ? transition state ? intermediate
• Intermediate ? transition state ? product

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Rate-Determining Step

• Reaction intermediates are stable as long as they
• dont collide with another molecule or atom,
• but they are very reactive.

Trapping agents are used to determine intermediate
Transition states are at energy maxima.
The reaction step with highest Ea will be the
slowest,
therefore rate-determining for the entire
reaction.
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Reaction Coordinate Diagram
The course of a reaction can be illustrated by
means of a reaction coordinate diagram. The
Transition State is the point of highest energy
along the minimum energy trajectory (i.e., the
reaction coordinate) of a reaction. The Energy of
Activation is defined as the energy required to
attain the Transition State.
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Transition State and Reaction Velocity
?Gfinal - ?Ginitial constant
?Gactivation has changed
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Prerequisites for chemical reactions

• The reactants must engage in an encounter
  (collision) event. The probability of encounter
  is dependent on reactant concentration (k2 108
  - 1011 M-1 s-1) and diffusion constants (or
  solvent viscosity). Note that k2 denotes the
  second-order rate constant.
• The encounter must proceed with the reactive
  functional groups aligned with proper orientation
  for reaction.
• The encounter must provide sufficient energy to
  surmount the "energy barrier" (Activation
  energy).
• Reaction spontaneity is determined by the Gibbs
  Free Energy a negative free energy is required
  for a reaction to occur spontaneously (ie. there
  is a decrease in free energy).

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Reaction Rate is Dependent on Activation Energy
Absolute Reaction Rate Theory predicts that the
rate of a chemical reaction is dependent on the
free energy of activation.
where kB 1.38
x 10-23J.K-1 is the Boltzmann constant, h 6.63 x
10-34J.s is Planck's constant. The exponent
includes the term for the Free Energy of
activation. Either an increase in temperature or
a decrease in the activation free energy will
result in an increase in reaction rate. For
example a decrease in the activation energy of 8
kcal/mol yields a 106 enhancement in rate.
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Catalysis Reduces ?G
A catalyst lowers the Energy of Activation but
does not alter reactant or product free energies.
The equilibrium constant is unchanged, although
both forward and reverse rates are enhanced.
A B C D
The equilibrium constant under standard
conditions, Keq, is defined as Keq
CD/AB ?G -RT ln Keq -2.303 RT log
Keq,
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First order reactions
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Pseudo first order reactions

• pseudo-first order concentration of one
  reactant remains essentially constant over time
  (often because it is in large excess compared to
  the other reagent)

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First order reaction with back reaction
Example conversion of aldehyde (A) to diol (D)
At equilibrium
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Arrhenius Equation and Transition State Theory
reactions occur as a sequence of elementary
steps. usually one of these steps is much slower
than the others ? Rate Determining
Step empirically, the effect of T on the rate of
this reaction step (and therefore on the overall
reaction rate) is described by the Arrhenius
equation
pre-exponential factor or frequency
factor describes collision frequency and the
orientation probability
Activation energy describes the fraction of
species with energy greater than Ea
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Activated complex or transition state theory
B C ? BC ? D E BC is the activated
complex or transition state maximum energy
barrier
k Boltzmann constant h Planks constant
Ea potential energy of activation, ?H is the
total
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II. Single-Molecule Biophysics

• This is an emerging and rapidly expanding field!
• This field has strong implications in many other
  areas!

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Why study biological processes at the
single-molecule level?

• Ensemble measurements ?average properties.
• Single-molecule methods can be used to study
• Distributions of observations
• Detection of multiple kinetic paths
• Transient intermediate states
• Time trajectories
• Conformational changes
• Underlying fundamental mechanisms
• In general, they can lead to quantitative
  understanding of complex biological phenomena.

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Single-Molecule Options

• Visualization structures (e.g., folding,
  assembly, oligomeric structure etc.)
• Probing forces (internal tensions, pressure,
  driving forces etc.)
• Probing mechanical work (e.g., protein motors)
• Probing motions and dynamics (e.g., frequency,
  folding-unfolding rates etc.)
• Probing diffusion coefficients (single-molecule
  diffusion in the cytosolic environment)
• Probing interactions (e.g., binding affinities in
  protein-ligand interactions, protein-DNA
  interactions, protein-protein-interactions)

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Question for September 27
Please calculate the enhancement in transition
rate induced by a decrease in activation free
energy of 1 cal/mol (eq. of one hydrogen bond).

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References for single-molecule biophysics
No textbooks available!!!
Just a chapter from 1. Methods in Modern
Biophysics Bengt Nöltig (Springer-Verlag,
Berlin Heidelberg, 2004).